T

Fig. 1.16 Heat flows between twe system s separated by a diathermal interface and encased in a rieid adiabatic boundary

Figure 1.16 shows two systems, called heat reservoirs, labeled 1 and 2, in good thermal contact through a heat-transmitting interface. Taken together, the pair constitutes an isolated system because the encasing boundary is both rigid and adiabatic.

No work is done by system 1 on system 2 (or vice versa) but because T1 ^ T2, heat flows from one system to the other. The direction of the arrows in the diagram follows the convention of the heat in the First Law, but one of the Qs must be negative. The First Law for the combined system is:

so that Q1 = -Q2.The First Law cannot predict which heat is negative; common experience and the Second Law require that heat flows from the hotter to the colder system, but this remains to be proven.

1.9 The Second Law of Thermodynamics

Textbooks on thermodynamics with a mechanical engineering flavor introduce the Second Law by considering the nature of heat and work in cyclical processes known as heat engines. Historically, this is indeed how the Second Law was first made quantitative and, as a byproduct, the thermodynamic property called entropy emerged. In these notes, the process is reversed. The Second Law in its several guises is first presented in the final forms that are close analogs of the forms of the First Law in Sect. 1.9. The relationship of heat engines and cyclical processes to the Second Law and entropy is deferred until Chap. 4.

We all have an intuitive feeling for the Second Law, but rarely make the explicit connection. We know, for example, that without any external intervention, heat will never flow from a cold body to a hot one, steam will not spontaneously decompose into H2 and O2, and Humpty Dumpty cannot be put together again. The opposite of these processes, which we know to be correct, cause the entropy of the universe to increase, which is precisely what the Second Law requires of spontaneous changes.

In the microscopic view of thermodynamics, entropy characterizes the state of disorder of a system. Since heating a system usually increases creates a less highly-ordered state, entropy changes are closely related to heat, but are not at all associated with work. The work that raises a weight by a frictionless pulley does not affect the state of order or organization of the system or the surroundings, and so work is entropy-neutral. This qualitative notion of the connection of heat and entropy is embodied in the following quantitative statement of the Second Law:

where AS and the integral represent changes from an initial state to a final state. The subscript "rev" means that the process must be reversible, not just in heat transfer but in the mechanical aspects as well (see Sect. 1.8). The last equality in Eq (1.16) is the special case of heat transferred at a constant temperature.

Entropy as a thermodynamic property was discovered well before the advent of quantum mechanics or Boltzmann's famous S = klnW. Following many years of investigation in the mid-nineteenth century, the German physicist Rudolph Clausius "discovered" Eq (1.9) in much the same way that the First law was revealed; namely, by examining the heat and work exchanged between a system and its surroundings as the system changed from one state to another. There are innumerable paths that a system can take between two end states, each path involving different values of Q and W. The internal energy difference AU is inferred from the invariant values of the Q - W for all paths. Being a thermodynamic property change, AU does not depend on the path taken.

In analogous fashion, Clausius showed that the integral jSQ/T is also the same for all processes between fixed end states, with the additional proviso that the processes are reversible.

The inescapable conclusion of this observation is that JSQ/T is the change in a thermodynamic property, which Clausius named entropy. A more detailed yet quite readable exposition of the method described above for uncovering the meaning of entropy is given in Van Ness' book (Ref. 2, pp. 55 - 61). Von Baeyer's book (Ref. 1, Chap. 7) gives a less technical recounting of Clausius' role in this search.

Equation (1.9) is the Second Law analog of Eq (1.4) for the First Law; both relate changes in a thermodynamic property to heat and work. In Eq (1.9), the convention for the sign of the heat is the same as that adopted for the first law: Q is positive if heat is added to the system.

Although Eq (1.4) applies to any process, Eq (1.9) is valid only for reversible changes. The complete statement of the Second Law that complements Eq (1.9) accounts for irreversible processes by the inequality:

Do we really want the one thing that gives us its resources unconditionally to suffer even more than it is suffering now? Nature, is a part of our being from the earliest human days. We respect Nature and it gives us its bounty, but in the recent past greedy money hungry corporations have made us all so destructive, so wasteful.